To determine the maximum allowable mass the cable can support, we first need to follow these steps:

1. Convert the cable diameter into radius:

The diameter of the cable is given as 10 cm, so the radius $r$ is: $r = \frac{10}{2} = 5 \, \text{cm} = 0.05 \, \text{m}$

2. Calculate the cross-sectional area:

Assuming the cable has a circular cross-section, its area $A$ can be calculated using the formula for the area of a circle: $A = \pi r^2$ Substituting $r = 0.05 \, \text{m}$: $A = \pi (0.05)^2 = 7.854 \times 10^{-3} \, \text{m}^2$

3. Determine the allowable stress:

The allowable stress $\sigma_{\text{allowable}}$ is the strength of the material divided by the factor of safety $FS$: $\sigma_{\text{allowable}} = \frac{\sigma_{\text{material}}}{FS} = \frac{1018.6 \, \text{MPa}}{2} = 509.3 \, \text{MPa}$ Converting this into pascals (since $1 \, \text{MPa} = 10^6 \, \text{Pa}$): $\sigma_{\text{allowable}} = 509.3 \times 10^6 \, \text{Pa}$

4. Calculate the maximum allowable force:

The maximum allowable force $F_{\text{max}}$ is given by: $F_{\text{max}} = \sigma_{\text{allowable}} \times A$ Substituting the values for $\sigma_{\text{allowable}}$ and $A$: $F_{\text{max}} = (509.3 \times 10^6) \times (7.854 \times 10^{-3}) = 4.000 \times 10^6 \, \text{N}$

5. Determine the maximum allowable mass:

The maximum allowable mass $m_{\text{max}}$ is related to the maximum force by the equation: $F_{\text{max}} = m_{\text{max}} \times g$ where $g$ is the acceleration due to gravity (approximately $9.81 \, \text{m/s}^2$). Solving for $m_{\text{max}}$: $m_{\text{max}} = \frac{F_{\text{max}}}{g} = \frac{4.000 \times 10^6}{9.81} \approx 407,749.74 \, \text{kg}$

Conclusion:

The maximum allowable mass the cable can support is approximately 407,750 kg.

Would you like more details or have any questions?

5 Related Questions:

1. How does the factor of safety affect the allowable stress in the cable?
2. How would a different material strength change the maximum allowable mass?
3. What would happen if the factor of safety was reduced?
4. How can we design a cable to support more weight while keeping the same diameter?
5. How would environmental factors, such as temperature, affect the cable’s strength?

Tip:

When designing with factors of safety, always ensure to consider dynamic loads and environmental conditions for maximum safety.